for which the Hamiltonian exhibits, as we will show, Anderson localization, i.e. exponentially decaying eigenfunctions. We present one method in Subsection REF  originally due to Bourgain [1]}, which applies to the Hamiltonian (REF ) in a very general sense and one more refined approach in Subsection REF  for a special case of the anti-chiral Hamiltonian that goes back to ideas of Jitomirskaya [2]}. The latter approach has been originally introduced for the almost Mathieu operator and applies to a larger range of Moiré length scales. The first approach has been extended to the matrix-valued setting by Klein [3]}. Both approaches also imply dynamical localization
\(\sup _{t>0} \left( \sum _{n \in \mathbb {Z}} (1+n^2) \Big \vert (e^{itH} \psi )(n) \Big \vert ^2 \right)^{1/2} < \infty ,\) 
